1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Hydrodynamics : Calculate force exerted by fluid on Tube

  1. Oct 27, 2012 #1
    1. The problem statement, all variables and given/known data

    A tube of uniform cross-section [itex]A[/itex] is bent to form a circular arc of radius [itex]R[/itex], forming three quarters of a circle. A liquid of density [itex]\rho[/itex] is forced through the tube with a linear speed [itex]v[/itex]. Find the net force exerted by the liquid on the tube.

    2. The attempt at a solution

    The centripetal force acting on a small element of [itex]dm[/itex] mass will be

    [tex]dF=\frac{v^2}{R}dm=\frac{\rho v^2}{R}dV=\frac{\rho A v^2}{R}dl[/tex].

    Integrating with proper limits, I got

    [tex]F=\frac{\rho A v^2}{R}\int_{0}^{3\pi R/2}dl=\frac{3\pi A \rho v^2}{2}[/tex]

    However the answer provided in my book is [itex]\sqrt{2} \rho Av^2[/itex] .What am I doing wrong. Can someone guide me?
     
  2. jcsd
  3. Oct 27, 2012 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    It says 'net force', but you added all the outward radial forces by magnitude, not as vectors. In fact, the shape doesn't matter. All you need to know is the direction of the flow at entry and exit. What is the change in momentum?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Hydrodynamics : Calculate force exerted by fluid on Tube
Loading...